An introduction to mathematics, by A. N. Whitehead.

COORDINATE GEOMETRY 117
ables, we may conceive them as correlated by
the equations x+y = 1, or by x +y = 1, or in
any one of an indefinite number of other ways.
This at once leads to the application of the
idea of algebraic form. We think, in fact, of
any correlation of some interesting type, thus
rising from the initial conception of variable numbers to the secondary conception of
variable correlations of numbers. Thus we
generalize the correlation x+y =l, into the
correlation ax + by =c. Here a and b and c,
being letters, stand for any numbers and are
in fact themselves variables. But they are
the variables which determine the variable
correlation; and the correlation, when determined, correlates the variable numbers x and
y. Variables, like a, b, and c above, which
are used to determine the correlation, are
called "constants," or parameters. The use
of the term "constant" in this connection
for what is really a variable may seem at first
sight to be odd; but it is really very natural.
For the mathematical investigation is concerned with the relation between the variables
x and y, after a, b, c are supposed to have
been determined. So in a sense, relatively to
x and y, the "constants" a, b, and c are constants. Thus ax +by = c stands for the general
example of a certain algebraic form, that is,
for a variable correlation belonging to a certain class.